Unveiling Quantum Phase Transitions and Constructing the Order Parameters in Interacting Quantum Many-body Systems with Unsupervised Machine Learning

Quantum phase transitions (QPTs) is one of the most active research fields in condensed matter physics. Understanding quantum phase transitions is essential for comprehending exotic condensed matter phenomena like topological materials andunconventional superconductors. However, identifying the quantum phase transition and characterising the quantum phases in interacting many-body systems remains a challenging task. The conventional technique depends on Landau's symmetry-breakingtheory, which is based on the concept of local order parameters. However, determining a suitable order parameter that defines the transition is a difficult operation that necessitates prior knowledge of the symmetry of the system. Due to the absence of preexistingsymmetry and the fact that the order parameter is often non-local, such a method is generally difficult to apply for systems that display topological phase transitions. Machine learning has recently emerged as a viable approach for identifying phase transitions in many-body systems without relying on empirical knowledge. Machine learning's strength rests in its capacity to discover features or structures in data without the need for explicit programming. Machine learning has been found to be able to recognise phase transitions in a variety of simple classical and quantum models. However, characterization of topological phase transitions or phases without a local order parameter, particularly in interacting quantum many-body systems, is still a work in progress. This proposed research has two main goals: 1) To use unsupervised machine learning techniques to identify QPTs in interacting many-body systems, particularly those with topological phases or phases without a local order parameter; 2) To derive the potentialorder parameter of various quantum phases with the aid of machine learning. Specifically, the autoencoder, a machine that is trained to best reconstruct the input in its output layer through learning an effective representation of the input data at a reduced dimension, will be used. The trained machine's ability to transfer the learned knowledge to other previously unseen models and thus its capability to play the role of an order parameter will also be investigated. The proposed study will contribute to the development of new tools for analysing QPTs in interacting quantum many-body systems, as well as the application of machine learning to address condensed matter physics challenges. This may also pave the way for future technological advancements, particularly in the field of quantum information science, where the topological state of matter may enable quantum computation.